The mean: simply average?

Posted on 22nd October 2014 by Ashline Amilcar

Calculating the mean is easy

The mean is one of the most used methods to summarize data. It is quite easy to calculate: the sum of the values of the entries divided by the count of these entries.

How to calculate the mean

But..

The mean is not located in the data set!

As seen above, the mean is not a value of the data set. When we read that the mean of children per family is 1.86, we immediately think that it’s impossible to have 0.86 children. So even when a list of data contains only entire numbers, their average is not necessarily an entire number.

0.67 children?

Above the mean, below the mean….

As a measure of central tendency, the mean is not a point that divides data in two halves, the median does. The amount of values located above or below the mean are not necessarily the same. The mean can be defined as the value that each participant would receive if the sum is divided equally among all members in a group. It is a point where the data’s values are balanced, just like a seesaw.

The mean is not the median

The extreme values

The mean is affected by extreme values. It’s more obvious when talking about the average of income. For example many countries have a lot of people whose income is low but with a few people earning a lot. The mean of the population income tends to rise for just 1 person who has an extremely high income. In certain cases, the mean might not be the most representative measure of data.

Distorted by extreme values

The mean of the mean

When you have more than one mean, be aware of their weights when calculating the mean of them. For example a class divided in three sections of 15, 15, and 30 students. The average of section 1, 2 and 3 is 10, 5, and 20 respectively. What is the average of the class?

Calculating the mean when using more than one mean

The mean is just one way of calculating an average for a given data set. It doesn’t always gives us what we need, and at those times other methods, such as the median or mode, may be more useful.

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